J.- i'm actually going through a very similar situation with my 5 year old step daughter. we have joint custody of her but she spends (thankfully) much more time with us than at her biological mother's. the hardest thing for us is trying not to blame her mother when catching her in a lie b/c we know that her mother lies and we cannot ever take anything she says at face value (much like your child's dad). i want to tell our daughter that i don't want her to end up like her mother but i know that is not an option. instead, we try very hard not to say anything bad about her mother as it isn't fair for us to manipulate her opinion of her. (she can make her own mind up when she's older).
i've really thought long and hard about this. before the Bible and before Christianity families taught their children right from wrong and held them accountable for moral decisions...so why am i having so much trouble?!
that said, i've tried a few things...in addition to taking toys away, time out (which doesn't seem to work at all for us) and other things. i've repeated the story of "the boy who cried wolf" time and again, emphasizing that no one believed him because he hadn't been honest. i try to remind her that if she isn't honest then others will not trust her. we have also bought and read a few children's books about basic behavior, kindness, patience, that sort of thing and i think they might be helping. she still tries to get away with occasional lies and ALWAYS displays the same behaviors to give herself away (hands up around her face and mouth, averted eyes, even her voice changes slightly!) but i think she is catching on and she knows that lying gets her into more trouble than it's worth.
best of luck to you. it's difficult to understand why a loving child would feel compelled to be dishonest. i think it's just a way of exploring their new found ability to fabricate stories. something else to think about it how to foster that creativity and teach them to the difference between "joking" and "lying" and telling interesting stories... geez, who knew parenting could be so demanding!